Chaotic Maps: A Tool to Enhance the Performance of OFDM Systems

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1 Chaotc Maps: A Tool to Ehace the Performace of OFDM Systems E. M. El-Bakary, O. Zahra, S. A. El-Doll, ad F. E. Abd El-Same Departmet of Electrocs ad Electrcal Commucatos Egeerg, Faculty of Electroc Egeerg, Meoufa Uversty, Meouf 395, EGYPT. 54 Abstract: Ths paper presets a chaotc terleavg approach for effcet data trasmsso wth orthogoal frequecy dvso multplexg (OFDM) over fadg chaels. The bary data s terleaved wth the proposed approach pror to the modulato step. The chaotc Baker map s used the proposed terleavg approach. I addto to reducg the chael effects o the trasmtted data, the proposed chaotc terleavg approach adds a degree of ecrypto to the trasmtted data. The performace of the proposed approach s tested by the trasmsso of mages over Raylegh fadg chaels wth chaotc terleavg. Expermetal results show that mages are receved wth hgher peak sgal to ose ratos (PSRs) f chaotc terleavg s appled. Keywords: Adaptve modulato, orthogoal frequecy dvso multplexg (OFDM), chael codg, bt error rate(ber), throughput. 1. Itroducto OFDM s a multcarrer modulato techology whch has effcet spectrum utlzato to support the trasmsso of hgh data rates [1,]. Trasmsso of mages ad multmeda wth the OFDM techology has attracted the atteto of several researchers [3-7]. Furthermore, several codg techques have bee vestgated for effcet trasmsso of mages wth OFDM over wreless chaels [3,4]. Despte the effcecy of these codg techques, they add much redudacy to the trasmtted data leadg to lower chael utlzato. Aother vestgated approach for effcet trasmsso of mages s the adaptve OFDM [5]. I ths approach, the subcarrer mappg s performed accordg to the chael codtos by usg a chael estmato algorthm. Although ths approach takes the chael codtos to cosderato, t s dffcult to sese the chael codtos at the trasmtter ad to perform chael estmato before data trasmsso. To avod the complexty of the chael estmato at the trasmtter, Salah et al. have proposed a adaptve OFDM scheme whch does ot requre chael estmato at the trasmtter [6]. Ths scheme s based o usg a uequal cyclc tme guard (UTG) wth OFDM. Ths scheme has succeeded achevg a good performace at hgh sgal to ose ratos (SRs). At low SRs, the eed for codg was uavodable. The falure of ths scheme to operate at low SRs wthout strog codg techques has lmted ts applcablty. The evoluto of multple put multple output (MIMO) ad beamformg techques wreless commucatos has opeed a ew feld of research for effcet mage trasmsso over wreless chaels [7,8]. MIMO techques ca mprove the effcecy of mage trasmsso through the addto of dversty to the system. Beamformg ca be used for terferece reducto. Theses ew techologes ca acheve a hgh effcecy mage trasmsso systems but wth creased complexty ad cost. Aother approach whch wll be cosdered ths paper s the performace ehacemet of mage trasmsso systems through data terleavg. It s kow that mage trasmsso over wreless chaels may face severe adverse codtos, especally burst errors where errors are lkely to occur clusters. To reduce the effect of these burst errors, bary data terleavg of the mages pror to modulato s requred [9-11]. There are some smple terleavg techques such as block terleavg [1,13]. The performace of such smple terleavers s lmted. Therefore, there s a eed for more powerful terleavers. Chaotc maps ca be used to buld strog terleavers. Thus, ths paper, a chaotc terleaver scheme based o chaotc Baker map s troduced. The proposed terleaver s appled to the mage bary format pror to modulato. Due to the strog terleavg ablty of chaotc maps, the proposed approach ca combat the chael effects wthout a eed for complcated codg schemes for error detecto ad correcto or adaptato the modulato scheme. Aother advatage of the proposed chaotc terleavg scheme s that t acheves a degree of ecrypto the trasmtted data whch adds more securty to the mage trasmsso process. Ths paper s orgazed as follows. Secto provdes a overvew of the OFDM system model used for mage trasmsso. Secto 3 dscusses the chael characterstcs OFDM systems. Secto 4 presets the fudametals of the chaotc Baker map. Secto 5 explas the proposed OFDM system model wth chaotc terleavg. The smulato results are preseted Secto 6. Fally, Secto 7 gves the cocludg remarks.. OFDM SYSTEM MODEL OFDM s oe of the most powerful commucato techologes whch are mplemeted curret wreless commucatos systems. I OFDM, the trasmtted hghspeed data s coverted to parallel data of subchaels [1,]. The, the trasmtted data of each parallel subchael s modulated by a adequate modulato scheme lke quadrature phase shft keyg (QPSK). These modulated data are fed to a verse fast Fourer trasform (IFFT) to geerate the multcarrer OFDM sgal. I order to avod the tersymbol terferece (ISI) whch occurs multpath

2 55 chaels, guard tervals are serted betwee frames [1,]. The block dagram of the tradtoal OFDM system s show Fgure (1). Fgure. Addto of the CP to a OFDM symbol. Whe the guard terval s loger tha the chael mpulse respose or the multpah delay, the effect of the ISI ca be elmated. However, the tercarrer terferece (ICI) or the -bad fadg stll exsts. The rato betwee the guard terval ad the usual symbol durato s applcato depedet, because the serto of a guard terval wll reduce the data throughput. After the serto of the guard terval, the trasmtted OFDM sgal s gve by [14]: (a) Trasmtter. s'( = d( k)exp( jπf ( t kt 1 k = = 0 f '( t kttotal ) total where d(k) s the data sequece ad f '( s the modfed pulse waveform of each symbol whch s defed as[14]: )) () 1 '( = 0 ( T g ( t < T t T ) f (3) g s, t > T ) s (b) Recever. Fgure 1. OFDM System Model. Guard tervals are ether the form of added zeros or a cyclc prefx (CP). The addto of a CP s the most wdely used approach. The key for makg OFDM realzable practce s the use of the fast Fourer trasform (FFT) ad the verse fast Fourer trasform (IFFT), whch have low complexty. I order for the IFFT/FFT to create a ISI-free chael, the chael must appear to provde a crcular covoluto [1,]. Addg a CP to the trasmtted sgal, as show Fgure (), eables the crcular covoluto property of the chael. If the mum chael spread delay has a durato of v+1 samples, addg a guard bad of at least v samples betwee OFDM symbols makes each OFDM symbol depedet of those comg before ad after t, ad so oly a sgle OFDM symbol ca be cosdered. If we assume that the symbol tme s T s, ad the CP tme s T g, the total symbol durato wll be [1,]: T total =T g +T s. (1) The OFDM sgal s the trasmtted through the chael. The trasmtted data s '( s the affected by a multpath fadg chael ad cotamated by addtve whte Gaussa ose (AWG). The receved sgal s defed as [14]: 0 r( = h( ) s'( t τ ) dτ + ( τ (4) where h (τ ) s the mpulse respose of the rado chael at tme τ, ad ( s the AWG. The receved sgal r ( s fltered by a badpass flter, whch s assumed to have a suffcetly wde passbad to avod dstortg the sgal. The guard terval s the removed ad a orthogoal detector s appled to the sgal order to obta the Fourer coeffcets of the sgal the observato perods. The output d ˆ ( k ) of the FFT crcut of the th OFDM subchael s gve by [14]: Ts + kttotal dˆ ( k) = 1/ Ts r( exp( jπ f( t kttotal )) dt (5) kttotal 3. Raylegh Fadg Chael The chael OFDM s characterzed by varous obstacles ad reflectos whch have a large fluece o the sgals durg the propagato of rado waves from the base stato to the moble stato. The rado waves trasmtted from a base stato radate all drectos, ad hece the recever receves may reflected waves from varous obstacles, dffracted waves, scattered waves ad the drect waves from the base stato. Sce the path legths of the drect, reflected, dffracted, ad scattered waves are dfferet, the

3 56 travel tme for each wave order to reach the moble stato wll be dfferet as well. Furthermore, the phases of the comg waves vary because of reflectos. As a result, the recever receves a superposto of several where B( r, s) are the ew dces of the data tem at ( r, s), M r < M +, 0 < s < M ad M = I steps, the chaotc terleavg s performed as follows: waves havg dfferet phases ad arrval tmes. The recepto evromet that s characterzed by a superposto of delayed waves s called a multpath propagato evromet. I a multpath propagato evromet, the receved sgal s sometmes tesfed or weakeed. Ths pheomeo s called multpath fadg ad the sgal level of the receved wave chages from momet to momet. The multpath fadg rases the error rate of the receved data [14]. Let us beg wth the mechasm by whch fadg occurs. The delayed wave wth cdet agle θ s gve by [14]: [ e ( exp j(πf )] r ( Re t = (6) where Re[ ] dcates the real part of a complex umber that gves the complex evelope of the comg wave from the th drectos of a multpath chael. e ( s geerated from the propagato path wth legth L betwee the base stato ad the moble stato ad t s gve by [14]: e ( c ( L ν t θ ) π cos ( exp j λ + φ = R (7) 1. A M M square matrx s dvded to k vertcal rectagles of heght M ad wdth.. These vertcal rectagles are stretched the horzotal drecto ad cotracted vertcally to obta a M horzotal rectagle. 3. These rectagles are stacked as show Fgure (3-a), where the left oe s put at the bottom ad the rght oe at the top. 4. Each M vertcal rectagle s dvded to boxes of dmesos M= cotag exactly M pots. 5. Each of these boxes s mapped colum by colum to a row as show Fgure (3-b). Fgure 3 shows a example of chaotc terleavg of a (8 8) square matrx. The secret key, S key = ( 1,, 3 ) = (, 4, ). R ad Ф are the evelope ad the phase of the th comg wave, respectvely, υ s the speed of moble stato (m/s), ad λ s the wavelegth. The th comg wave has a shft the carrer frequecy by the Doppler shft f d (Hz), whch s descrbed as [14]: f d ( v / λ) cos( θ ) = (8) It has a mum value of υ/λ, whe the comg wave comes from the rug drecto of the moble stato at cos(θ ) = 1 [14]. It s oted that, the evelope fluctuatos follow a Raylegh dstrbuto, whle the phase fluctuatos follow a uform dstrbuto. These Raylegh dstrbuto fluctuatos of the evelope deterorate the receved sgals, severely. So, there s a eed for a strog terleavg mechasm to reduce the effect of fadg o the receved sgals. 4. CHAOTIC ITERLEAVIG Fgure 3. Chaotc terleavg. (a) Dscretzed Baker map. (b) Radomzato of a 8 8 block. 5. THE PROPOSED OFDM SYSTEM MODEL The proposed mage trasmsso OFDM system model ths paper cossts maly of 3 stages whch are a mage data formattg stage, a chaotc terleavg stage whch s performed o the bary mage data, ad a OFDM modulato stage. The block dagram of the proposed system model s show Fgure (4). At the trasmtter, the chaotc terleavg s appled to the mage ts bary format, ad hece the mage bary data s radomzed before the OFDM modulator step. The steps of the proposed OFDM system model ca be summarzed as follows: The Baker map s a chaotc map that geerates a permuted verso of a square matrx. I ts dscretzed form, the Baker map s a effcet tool to radomze a square matrx of data. The dscretzed map ca be represeted for a M M matrx as follows [15-0]: B( r, s) M ( r M ) M M + s mod, s s mod + M M (9) = Fgure 4. Block dagram of the proposed OFDM system model.

1. The mage s trasformed to the bary format, pxel by pxel, matrx form.. The o-square bary matrx s reshaped to a M M square structure. 3. Chaotc radomzato s appled to ths square matrx. 4.

4 1. The mage s trasformed to the bary format, pxel by pxel, matrx form.. The o-square bary matrx s reshaped to a M M square structure. 3. Chaotc radomzato s appled to ths square matrx. 4. After the radomzato process, the square bary matrx s reshaped aga to ts orgal dmesos. 5. A OFDM modulato step s performed o the bary data. 6. At the recever, after the OFDM demodulato step, the receved bary data s reshaped aga to a square matrx ad chaotc deradomzato s appled to ths matrx 7. The square bary matrx after deradomzato s reshaped aga to ts orgal dmesos. 8. The mage s retreved from the bary data. 6. SIMULATIO RESULTS I ths secto, smulato expermets are performed to test ad evaluate the proposed chaotc terleavg scheme ad to compare t wth ormal OFDM. The PSR s used to measure the qualty of the recostructed mages at the recever. It s defed as follows: f PSR = 10 log 10 (10) MSE Fgure 5. The receved Lea mage usg OFDM wth ad wthout chaotc terleavg. E b / 0 = 0 db ad f d =30 Hz. 57 where f s the mum possble pxel value of a mage f. For 8 bt pxels, f =55. The MSE refers to the mea square error betwee the orgal mage ad the receved mage. For a moochrome mage, the MSE s defed as follows: [ f (, fˆ(, ] = 1 j= 1 MSE = (11) where f (, s the orgal mage, ad f ˆ(, s the receved mage. I the frst expermet, Lea mage s trasmtted usg OFDM wth ad wthout chaotc terleavg wth a bt eergy to ose rato E b / 0 = 0 db over a sgle path Raylegh fadg chael the presece of addtve whte Gaussa ose (AWG). QPSK s used for basebad modulato. 18 subcarrers are used OFDM ad a guard terval legth = 1/4 of the symbol durato s mplemeted. The results of ths expermet are show Fgure (5). It s clear from these results that the use of OFDM wth chaotc terleavg creases the PSR the recostructed mage by about 6 db. Two other expermets are performed o the Lea mage but wth E b / 0 = ad 4 db, respectvely. The results of these expermets are show Fgures (6) ad (7), respectvely. These results reveal the superorty of the proposed OFDM trasmsso scheme wth chaotc terleavg to that wthout chaotc terleavg. Three other expermets are also performed o the Camerama mage ad ther results are tabulated Table 1. These results also reveal the superorty of OFDM wth chaotc terleavg to ormal OFDM wthout terleavg. Fgure 6. The receved Lea mage usg OFDM wth ad wthout chaotc terleavg. E b / 0 = db ad f d =30 Hz.. E b / 0 (db) 0 4 PSR (db) ormal OFDM PSR (db) OFDM wth chaotc terleavg Table 1. Results of the trasmsso of the Camerama Image Fgure 7. The receved Lea mage usg OFDM wth ad wthout chaotc terleavg. E b / 0 = 4 db ad f d =30 Hz.

5 58 7. COCLUSIOS [13] V. D. guye, H. P. Kuchebecker, " Block terleavg for soft decsol Vterb decodg OFDM A effcet chaotc terleavg scheme has bee systems", Proceedgs of the IEEE Vehcular Techology preseted for wreless mage trasmsso wth OFDM. Ths Coferece(VTC), pp , 001. terleavg scheme s based o the chaotc Baker map. The [14] H. Harada ad R. Prasad, Smulato ad Software terleavg process s appled to the bary mage data pror Rado for Moble Commucatos, Artech House to the modulato step. The proposed scheme mproves the Publshers, 00. performace of the OFDM system, where t geerates [15] F. Ha, X. Yu,. ad S. Ha, " Improved Baker Map for permuted sequeces wth lower correlato betwee ther Image Ecrypto", Proceedgs of the Frst Iteratoal samples. The performace of the proposed scheme was Symposum o Systems ad Cotrol I Aerospace ad studed over a Raylegh multpath fadg chael ad the Astroautcs, ISSCAA 006, pp obtaed results show a otceable performace [16] J. Frdrch, "Image Ecrypto Based o Chaotc mprovemet over ormal OFDM. Maps", Proceedgs of the IEEE Iteratoal Coferece REFERECES o Systems, Ma, ad Cyberetcs, 1997, pp [17] Q. Qa, Z. Che, Z. Yua, "Vdeo Compresso ad [1] J. G. Adrews, A. Ghosh ad R. Muhamed, Ecrypto Based-o Multple Chaotc System", Fudametals of WMAX, Pearso Educato, Ic Proceedgs of The 3rd Itetatoal Coferece o [] W. Webb, Wreless Commucatos: The Future, Joh Iovatve Computg Iformato ad Cotrol Wley & Sos Ltd, 007. (ICICIC'08). [3] M. Khedr, M. Sharkas, A. Almaghrab ad O. Abdelaleem, " A SPIHT/OFDM wth Dversty Techque for Effcet Image Trasmsso over Fadg Chaels", Proceedgs of the IEEE Iteratoal Coferece o Wreless Commucatos, etworkg ad Moble Computg (Wcom), pp , 007. [4] J. fag, M. H. Lee, M. Jag ad J Y. Park, " Robust Wreless Image Trasmsso Based o Turbo-Coded OFDM", IEEE Trasactos o Cosumer Electrocs, Vol. 48, o. 3, pp , 00. [5] H. S. Chu, B. S. Park, C. K. A, J. S. Kag; H. G So, " Wreless mage trasmsso based o adaptve OFDM system", Proceedgs of the IEEE Iteratoal Forum o [18] F. Huag, F. Le, "A ovel Symmetrc Image Ecrypto Approach Based o a ew Ivertble Twodmesoal Map", Proceedgs of the Iteratoal Coferece o Itellget Iformato Hdg ad Multmeda Sgal Processg IIHMSP 008, pp [19] S. C. Koduru ad V. Chadrasekara, "Itegrated Cofuso-Dffuso Mechasms for Chaos Based Image Ecrypto", IEEE 8th Iteratoal Coferece o Computer ad Iformato Techology Workshops, 008, pp [0] K. Usma, H. Juzojl ad I. akajmal, "Medcal Image Ecrypto Based o Pxel Arragemet ad Strategc Techology, IFOST, pp.63-66, 007. Radom Permutato for Trasmsso Securty" [6] M.M. Salah, A. A. Elrahma, ad M. M. Mokhtar, Proceedgs of the 9 th Iteratoal Coferece o e- "Performace Ehacemet of Image Trasmsso Usg UEP Overlayed UTG_OFDM Scheme", Proceedgs of Health etworkg, Applcato ad Servces, 007, pp the 5th atoal Rado Scece Coferece (RSC), 008. [7] M. Farshcha ad W. A. Pearlma, " Real-Tme Vdeo Trasmsso Over MIMO OFDM Chaels Usg Space- Tme Block Codes", Proceedgs of the IEEE 40 th Aual Coferece o Iformato Sceces ad Systems, pp , 006. [8] T. Athaasads, K. H. L, ad Z. M. Hussa, " Multmeda Trasmsso over Wreless Space-Tme- Frequecy coded OFDM Systems wth Adaptve Beamformg", Proceedgs of the IEEE Asa-Pacfc Coferece o Commucatos (APCC), 006. [9] Y.Wag ad Q. F.Zhu, Error cotrol ad cocealmet for vdeo commucato: A revew, Proceedgs of the IEEE,Vol.86,pp , [10] C. K. Sug, J. Heo, ad I. Lee, Adaptve Bt- Iterleaved Coded OFDM wth Reduced Feedback Iformato, IEEE Trasactos o Commucatos, Vol. 55, o. 9, pp , 007. [11] S.W. Le ad V. K.. Lau Performace Aalyss of Adaptve Iterleavg for OFDM Systems, IEEE Trasactos O Vehcular Techology, Vol. 51, o. 3, pp , 00. [1] Y. Fag, L. Yu, " Block-Iterleaved Error-Reslet Etropy Codg", Proceedgs of IEEE Iteratoal Symposum o Crcuts ad Systems (ISCAS), pp

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